Question

Suppose you win the Powerball lottery this​ year, which is worth ​$600 million. You can choose to take a lump sum now of $575 million or you can​ "annuitize" your winnings. Annuitization means that you will receive the total jackpot money in 5 equal annual payments of ​$120 starting next year.

If the interest rate is 2.5 percent, the present value of the 5 equal payments is ​$______ million.

Answer 1

The present value of the 5 equal annual payments of $120 million from the Powerball lottery at an interest rate of 2.5% is approximately $556.75 million.

Step-by-step explanation:

The present value (PV) of the Powerball lottery annuitized payments can be found using the formula for the present value of an annuity. This calculation assumes regular payments and a constant interest rate over the period. To calculate the PV of 5 annual payments of $120 million at an interest rate of 2.5%, we use the formula PV = Pmt [((1 - (1 + r)^{-n}) / r)], where Pmt is the annual payment, r is the interest rate per period, and n is the number of periods (years).

Plugging the values into the formula, we get PV = $120 million [((1 - (1 + 0.025)^{-5}) / 0.025)], which simplifies to approximately $556.75 million as the present value of the annuity payments.